See [1]}.
Another useful fact is the Mecke formula for the random
connection model. Let \(s, \lambda >0\)  and suppose \(f(x,G) \in \mathbb {R}_+\)  is defined
for
all pairs \((x,G)\)  where \(G\)  is a finite graph with vertex
set \({\cal V}(G) \subset B(s)\)  and \(x \in {\cal V}(G)\) . Then whenever
the following expectations are defined we have
\({\mathbb {E}}\sum _{x \in {\cal H}_{\lambda ,s}} f(x,G({\cal H}_{\lambda ,s})) =\lambda \int _{B(s)} {\mathbb {E}}[f(x, G( {\cal H}_{\lambda ,s}^x))] dx\) 
